TY - GEN

T1 - On graphs supported by line sets

AU - Dujmović, Vida

AU - Evans, William

AU - Kobourov, Stephen

AU - Liotta, Giuseppe

AU - Weibel, Christophe

AU - Wismath, Stephen

N1 - Funding Information:
★ Research supported in part by: NSERC, MIUR under project AlgoDEEP prot. 2008TFBWL4. The research in this paper started during the McGill/INRIA Workshop at Bellairs. The authors thank the organizers and the other participants for useful discussions.
Funding Information:
Graphs Supported by Arrangements of Lines
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more "powerful" than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.

AB - For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more "powerful" than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.

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U2 - 10.1007/978-3-642-18469-7_16

DO - 10.1007/978-3-642-18469-7_16

M3 - Conference contribution

AN - SCOPUS:79952268624

SN - 9783642184680

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 177

EP - 182

BT - Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers

T2 - 18th International Symposium on Graph Drawing, GD 2010

Y2 - 21 September 2010 through 24 September 2010

ER -